Arsenal technical chief Andrea Berta has already held talks with agents for the Palace midfielder.
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The Gunners are getting serious about the 27 year-old, knowing they must burn off competition from Tottenham for the England international's signature.
Eze's contract carries a £68m buyout clause and Palace have so far referred all enquiries to the option.
The Sun says Berta hopes to convince Palace to part with Eze by offering a cash-plus-player proposal. It's suggested Berta knows Palace are seeking a defensive signing and will seek to include a young defender in Arsenal's offer.
No names have been mentioned, though Jakub Kiwior could be a candidate for the swap.